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be satis ed in the rise portion of the cam pro le The differences between this example and the rst are the displacement constraints at x = 36 deg and at x = 90 deg Figures 55 and 56 show the results obtained by applying both the conventional polynomial approach and the spline method with uniform spacing of the knots, exactly as was done in the rst example In both cases all the constraints are satis ed, but there is a dip in the velocity curve and a reversal of acceleration near the end of the rise This feature is more pronounced in the case of the polynomial function Fig 57 shows the result of adjusting the positions of the interior knots: the acceleration reversal is eliminated and the peak value of acceleration near 135 deg is reduced If there is a rational approach to the selection of knots to achieve a speci c effect in cases such as this, it has not yet been determined However, in general, it is possible to introduce local adjustments in the synthesized cam motion by making adjustments in the knot sequence Here, a simple trial-and-error procedure was used, and the results shown were obtained in only a few minutes The results shown were obtained with the interior knots at x = 50 deg, x = 95 deg, and x = 100 deg

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TABLE 21-12 Methods De ned by Array (continued)

Part II:

Displacement (cm) Velocity (cm/rad) Acceleration (cm/rad/rad) Constraint 1 0 45 90 Cam rotation angle (deg)

Often you will want to sort the contents of an array To handle this, Array supports a rich complement of sorting methods Using Sort( ), you can sort an entire array, a range within an array or a pair of arrays that contain corresponding key/value pairs Once an array has been sorted, you can efficiently search it using BinarySearch( ) Here is a program that demonstrates the Sort( ) and BinarySearch( ) methods by sorting an array of ints:

// Sort an array and search for a value using System; class SortDemo { static void Main() { int[] nums = { 5, 4, 6, 3, 14, 9, 8, 17, 1, 24, -1, 0 }; // Display original order ConsoleWrite("Original order: "); foreach(int i in nums) ConsoleWrite(i + " "); ConsoleWriteLine(); // Sort the array ArraySort(nums); // Display sorted order ConsoleWrite("Sorted order: foreach(int i in nums) ConsoleWrite(i + " "); ConsoleWriteLine();

FIGURE 54 Cam follower displacement, velocity, and acceleration obtained from cycloidal motion in Example 2

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// Search for 14 int idx = ArrayBinarySearch(nums, 14); ConsoleWriteLine("Index of 14 is " + idx); } }

The output is shown here:

TABLE 53 Cam angle (degrees) 000 360 900 1800

Original order: 5 4 6 3 14 9 8 17 1 24 -1 0 Sorted order: -1 0 1 3 4 5 6 8 9 14 17 24 Index of 14 is 9

In the preceding example, the array has an element type of int, which is a value type All methods defined by Array are automatically available to all of the built-in value types However, this may not be the case for arrays of object references To sort or search an array of object references, the class type of those objects must implement either the IComparable or IComparable<T> interface If the class does not implement one of these interfaces, a runtime exception will occur when attempting to sort or search the array Fortunately, both IComparable and IComparable<T> are easy to implement IComparable defines just one method: int CompareTo(object obj)

Constraints for Example 3 Displacement (cm) 000 001 060 100 Velocity (cm/rad) 000 000 Acceleration (cm/rad/rad) 000 000 000

21:

1 1

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